Imaging Based on a Fast Back-Projection Algorithm Considering Antenna Beamwidth

The Geosynchronous Satellite Synthetic Aperture Radar (GEO SAR) operates at a high orbital altitude, resulting in an extended imaging time and substantial variations in slant range. Additionally, the GEO SAR satellite orbit experiences a bending effect, and the target’s movement, caused by the Earth’s rotation, is influenced by the Earth’s curvature. The back-projection (BP) algorithm has been proven to be a highly effective technique for precise imaging with GEO SAR by processing these specific echo signals. However, this approach necessitates considerable computational resources. Existing BP algorithms, such as the fast BP algorithm, do not consider the “Stop-and-Go” error present in GEO SAR. Consequently, we developed a Precise Slant Range Model that considers the motion of both the satellite and targets. The model incorporates velocity and acceleration factors to accurately represent the signal transmission from transmission to reception. Additionally, we propose a Rapid Range History Construction Method to lessen the computational burden of generating the three-dimensional range history array. By utilizing the Precise Slant Range Model and the Rapid Range History Construction Method, and employing parallel processing through aperture segmentation, we propose an Accurate and Efficient BP imaging algorithm suitable for GEO SAR applications. To validate its effectiveness, simulations were conducted using the parameters of a GEO SAR system. The results indicated that the proposed algorithm enhances the imaging quality of GEO SAR, reduces the processing time, and achieves high-precision rapid imaging, thereby improving operational efficiency.

In squinted synthetic aperture radar (SAR) imaging, the range-azimuth coupling requires precise range cell migration correction (RCMC). Moreover, for high-resolution airborne SAR, motion compensation (MOCO) becomes complicated as the squint angle increases, thereby degrading the performance of Doppler-domain imaging algorithms. On the other hand, time-domain back-projection (BP) SAR imaging approaches are considered as optimal solutions to performing precise image focusing and MOCO. Among current BP algorithms, the fast factorized back-projection (FFBP) algorithm is one of the most essential representatives that achieve high-resolution images in an efficient manner. In this paper, the principle and applications of the FFBP algorithm are investigated through the derivation of the azimuth impulse response function (AIRF) of the resulting image. The phenomenon of spectrum displacement induced by motion errors in the BP image is presented and analyzed. Based on rigorous mathematical derivations, a modified FFBP algorithm is proposed to facilitate a seamless integration with motion compensation and accurate imagery of high-resolution highly squinted airborne SAR. Real data results confirm the effectiveness of the proposed approaches.

In this article, a novel sinogram decimation fast back-projection (SD-FBP) algorithm for strip-map synthetic aperture radar (SAR) imaging is proposed. We first review the back-projection (BP) and the fast factorized BP (FFBP) algorithms, then analyze the cause of the FFBP imaging degradation theoretically based on the combination of SAR imaging and the sinogram concept of computed tomography, illustrating that the degradation is much more severe for strip-map mode. Based on the SAR sinogram, the SD-FBP algorithm is proposed to mitigate the FFBP degradation for strip-map SAR imaging. The complexity of the SD-FBP is analyzed and compared with that of the FFBP and the Cartesian factorized BP (CFBP). The superiority of the SD-FBP algorithm is validated using the simulation and real spaceborne strip-map SAR data, e.g., Sentinel-1, Gaofen-3, and LuTan-1. The results show that the SD-FBP can tackle the FFBP imaging degradation for strip-map SAR, and runs faster than the FFBP and the CFBP.

This study presents a fast backprojection algorithm (FBPA) for bistatic forward-looking spotlight synthetic aperture radar (BFSSAR) imaging. It represents the subimages on the polar grids to reduce the computational burden. First, the backprojection algorithm for the BFSSAR imaging is introduced. Then, FBPA for the BFSSAR imaging based on the subaperture processing is provided, and the sampling requirements for the polar grids of subimages are derived from the bandwidth angle. Simulation results are shown to demonstrate its validity.

The back projection (BP) algorithm is highly effective in bistatic SAR imaging. But it is time-consuming for the large scene imaging. In this paper, we propose a GPU-based parallel BP algorithm, the range compression and back projection are implemented on the graphics processing unit (GPU) using CUDA language. We also present some optimum methods including memory optimization, phase accumulator reduction and imaging scene segmentation to implement fast and large scene imaging. Numerical experiments demonstrate that the GPU-based method can significantly improve the computational efficiency of the original BP algorithm, about 80 times faster, while the imaging scene size same as the CPU-based BP algorithm.

Microwave imaging technique is crucial to the through-wall radar and ground penetrating radar (GPR). Aim for these two important applications, the article presents a modified back-projection (BP) algorithm oriented for near-field two-dimensional (2D) microwave object reconstruction. The proposed synthetic BP scheme is a combination of BP algorithm and frequency-wavenumber domain methods. Complex backscattered signals are back projected to get a radar map, after compensating the curvature of the scatter field wavefront and the initial phase, the modified radar map is demonstrated to contain a copy of a certain rectangular part of the target spatial spectrum. Then multi-measurements are achieved to compose a synthetic spectrum by a multiple-input multiple-output (MIMO) array. The fast Fourier Transform (FFT) is applied to the synthetic spectrum to realize a high-quality imaging results. Numerical simulations demonstrate the image reconstruction performance, while show high cross-section resolution and fast computation speed at the same time. Associated sampling criteria, the feasibility for a larger field of view and reconstruction based on sparse MIMO array are also discussed.

Stepped frequency continuous wave ground penetrating radar (SFCW-GPR) systems are becoming increasingly popular in the GPR community due to the wider dynamic range and higher immunity to radio interference. The traditional back-projection (BP) algorithm is preferable for SFCW-GPR imaging in layered mediums scenarios for its convenience and robustness. However, the existing BP imaging algorithms are usually very computationally intensive, which limits their practical applications to SFCW-GPR imaging. To solve the above problem, a fast SFCW-GPR BP imaging algorithm based on nonuniform fast Fourier transform (NUFFT) technique is proposed in this paper. By reformulating the traditional BP imaging algorithm into the evaluations of NUFFT, the computational efficiency of NUFFT is exploited to reduce the computational complexity of the imaging reconstruction. Both simulation and experimental results have verified the effectiveness and improvement of computational efficiency of the proposed imaging method.

In order to solve the problems that the existing high squint missile-borne synthetic aperture radar( SAR) algorithm can not deal with too high squint angle,and that the calculated amount of traditional back-projection( BP) imaging algorithm is too large,as well as that the current fast BP algorithm can not process the echo data in parallel,an improved approximate forward looking missile-borne SAR back-projection imaging algorithm which can process echo data in parallel was proposed. According to geometrical relationship of approximate forward looking missile-borne SAR,an echo signal model was established. And the imaging area was divided to equidistance strip in range along the distance direction. The image was split when merging sub aperture,and the splitting and merging did not stop until the accuracy of image met the requirements.Next the raw echo data was back projected to each strip for coherent integration,and then the missile-borne SAR image was obtained. If these strips were processed for imaging in parallel,the imaging speed would be further improved. Finally,results of simulation echo data and real echo data validate that the improved algorithm can deal with approximate forward looking scene with 86° squint angle,and it can greatly improve the computation speed compared with that of traditional BP algorithm. Moreover,the computation speed is faster than that of other improved BP algorithms by processing those strips in parallel.

Circular synthetic aperture radar (CSAR) has a 360° observation capability on the central observation scenario. A typical way to process CSAR imaging is to cut data into small sub-apertures because most targets are only coherent at a very small observation angle. There are many sub-aperture imaging methods after development in recent years. The back-projection algorithm is widely used because it is simple and can be applied to an arbitrary trajectory. Because of the limitation of the Nyquist sampling frequency and influence of the antenna sidelobe, azimuth ambiguity is a phenomenon that may occur in the radar imaging process. The existing researches typically choose the back-projection (BP) imaging area according to the SAR platform flight path and the antenna beam width. The limitation of the CSAR imaging area and its azimuth ambiguity region are rarely analyzed theoretically. This paper focus on the sub-aperture imaging of CSAR, based on the BP algorithm, which derives the relationship of azimuth ambiguity with CSAR parameters such as the pause repeat frequency (PRF), slant range angle, velocity of radar platform, etc. This paper proposes an equation for the calculation of the azimuth ambiguity region and analyzes the limitations, which provides theoretical support for CSAR parameter design, imaging area selection, and azimuth ambiguity analysis.

This paper concerns the surface-tracing-based (STB) linear-array synthetic-aperture-radar (LASAR) 3-D imaging technique. The basic idea of this technique is to consider the 3-D SAR imaging problem as tracing a surface in the low height-resolution level. The STB 3-D imaging technique first initiates a low-resolution digital elevation map (DEM) using 3-D backprojection (BP) algorithm, predicts a higher resolution DEM from the known elevation using multivariate-interpolation technique, searches from the predicted elevation and obtains a higher resolution DEM, then repeats the prediction and searching recursively and obtains the fine-resolution DEM finally. By converting the 3-D LASAR imaging problem to a 2-D surface-tracing problem, the STB 3-D imaging technique can reduce the computational complexity by one order. The computational cost of STB 3-D imaging technique is analyzed, and we find out that the computational cost of STB 3-D LASAR imaging technique is determined by the surface prediction error and the fluctuation of ground. In particular, for normal distribution, when one of the earlier two factors is small, the computational cost is proportional to the other factor approximately. Finally, a new STB 3-D BP algorithm that implements the surface-prediction operation via multiresolution-approximation (MRA) technique (named as MRA 3-D BP algorithm) is presented. By operating the interpolation in frequency domain, the computational cost of MRA algorithm for sparse LASAR is near to that of RD algorithm for full-element LASAR.

Highly squint synthetic aperture radar (SAR) increases the flexibility and aspect-information of observation but poses several challenges to frequency-domain algorithms. The back-projection (BP) algorithm is recognized to produce the best results for highly squint mode but at high computational expense. Several fast BP algorithms have been developed to enhance the efficiency of the BP integral. The Cartesian factorized BP (CFBP) algorithm has been proposed to improve the performance. However, CFBP is ineffective in the highly squint case because its range model (RM) is imprecise. In this letter, we propose a modified CFBP (MCFBP) algorithm for highly squint spotlight SAR imaging. We employ a transformed Cartesian coordinate system to treat the transceiver mode as approximately side-looking mode. According to the transformed coordinate system, we propose a modified RM (MRM) to reduce the range error. Based on the MRM, we derive modified image spectrum compression steps and the Nyquist sampling rate of the subaperture image. MCFBP inherits CFBP's accuracy and efficiency advantages. Results of simulations and experiments performed by the X-band airborne SAR system with a maximum bandwidth of 1.2 GHz validate the improved performance of the proposed algorithm relative to BP and fast factorized BP.

Ground penetrating radar (GPR) is a promising non-destructive evaluation technique for detecting buried underground objects in urban area. Deep learning technique is recently being applied into this field to automate the GPR data interpretation. However, there is no proper technique that can reflect the uniqueness of urban road pavements. In this study, an underground object detection technique suitable for urban road pavement is proposed by using a statistically determined threshold amplitude and a large amount of GPR B-scan image libraries. An automated thresholding technique is newly developed based on the statistical distribution of GPR data. Deep learning technique is then applied to the reconstructed GPR data to detect underground objects in urban area. The proposed method is experimentally validated by field data collected on urban roads in Seoul, South Korea. In addition, its application possibility is also tested with full-size GPR data. The proposed method successfully emphasises the feature of underground objects and classifies hyperbola, manhole cover, layer interface and subsoil background.

The conventional digital beam forming (DBF) for conformal array needs to scan a series of look angles with small angular separation to obtain a high-resolution pattern. Inspired by the fast back projection algorithm (FBP)[3] for SAR imaging, a fast DBF algorithm for the conformal array is proposed in this paper. Firstly, the conformal array is divided into several subarrays, and the pattern of each subarray is formed in a coarse resolution. Then, the pattern of each subarray is interpolated to a high resolution one by FFT. Finally, all subarrays' high-resolution pattern is added together to form the pattern of the whole array. The simulation results have proved the efficiency and accuracy of the proposed algorithm.

The fast time-domain algorithm (FTDA) for the bistatic forward-looking synthetic aperture radar (BFSAR) imaging is presented in this paper. Here, the subimage is represented in the slant range plane instead of the ground plane. The FTDA includes the fast backprojection algorithm (FBPA) with the subaperture and elliptical polar grid processing, and the FBPA with the subaperture and polar grid processing. Experimental results are given to prove the validity of the proposed FBPA.

This paper proposes a study of a time-domain ground penetrating radar (GPR) signal by using the time- domain uniform geometrical theory of diffraction (UTD) method. The monostatic GPR system is employed in this study. Rays tracing method is employed to find the reflected ray and diffracted ray paths between the transmitting antenna (Tx) and the receiving antenna (Rx). Moreover, the conventional UTD method is adapted to calculate the frequency-domain transfer function of the electric field between Tx antenna and the Rx antenna. The medium including air, ground and underground objects are taken into account. Finally, the received time-domain GPR signal is obtained by using the inverse fast Fourier transform (iFFT) method. The calculated results found that the time-domain GPR signal can be calculated by using the time-domain UTD method. The ground reflection, object reflection and object diffraction time-domain signal can be separately calculated. The reflected signal from the ground and an underground curved object can be illustrated.